Quantization and Morita equivalence for constant Dirac structures on tori

Tang, Xiang; Weinstein, Alan

Annales de l'Institut Fourier, Tome 54 (2004) no. 5, pp. 1565-1580.

Nous définissons une quantification $C^{*}$-algebrique des structures de Dirac constantes sur les tores, et nous démontrons que l’équivalence à $O(n,n|\mathbb{Z})$ près des structures implique l’équivalence de Morita de leurs quantifications. Ce résultat complète et généralise un théorème de Rieffel et Schwarz, donné dans le cadre des structures de Poisson.

We define a $C^{*}$-algebraic quantization of constant Dirac structures on tori and prove that $O(n,n|\mathbb{Z})$-equivalent structures have Morita equivalent quantizations. This completes and extends from the Poisson case a theorem of Rieffel and Schwarz.

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